Safety-Critical Kinematic Control of Robotic Systems

Abstract

Over the decades, kinematic controllers have proven to be practically useful for applications like set-point and trajectory tracking in robotic systems. To this end, we formulate a novel safety-critical paradigm by extending the methodology of control barrier functions (CBFs) to kinematic equations governing robotic systems. We demonstrate a purely kinematic implementation of a velocity-based CBF, and subsequently introduce a formulation that guarantees safety at the level of dynamics. This is achieved through a new form of CBFs that incorporate kinetic energy with the classical forms, thereby minimizing model dependence and conservativeness. The approach is then extended to underactuated systems. This method and the purely kinematic implementation are demonstrated in simulation on two robotic platforms: a 6-DOF robotic manipulator, and a cart-pole system.

Passivity-Preserving Safety-Critical Control Using Control Barrier Functions

“…The class of CBFs that preserve passivity include those introduced by the authors in [10], which are associate to the so-called energy-based safety constraints. This fact, beyond providing a constructive way to guarantee passivity when computing kinematic tasks, reinforces the link between safety-critical and energy-based techniques, a duality stressed in [6] and explored further in this letter.…”

“…Lemma 1 [8], [10]: Let h(x) be a CBF on D for (1) and assume U = R m and L g h(x) = 0, ∀x ∈ D. Define (x; u des ) = ḣ(x, u des (x)) + α(h(x)). A closed-form solution for ( 6) is given by u * (x) = u des (x) + u safe (x), where…”

“…In the following we briefly introduce the relevant information involving passivity and safety-critical control. We refer to [2] for passivity and to [6], [7], [8], [10] for safetycritical control for references which completely cover the presented background.…”

Adaptive critic learning for event‐triggered safe control of nonlinear safety‐critical systems

“…Therefore, how to ensure the system safety becomes a major challenge. In recent years, control barrier func-tions (CBFs) have been shown to be effective in ensuring safety in systems [2,3], and it has been widely applied to robots [4,5], autonomous vehicles [6,7], and other safety-critical systems. These methods usually design the optimal safety controller by combining set invariance conditions and optimal control problems.…”

“…Thus, the safety and optimality of the system are guaranteed. For designing optimal safety controllers, most methods were based on the quadratic program (QP) framework [2][3][4][5][6][7][8]. However, the design scheme based on a QP has some problems.…”